butools.ph.CdfFromPH¶

butools.ph.CdfFromPH()¶

Matlab:	cdf = CdfFromPH(alpha, A, x)
Mathematica:	cdf = CdfFromPH[alpha, A, x]
Python/Numpy:	cdf = CdfFromPH(alpha, A, x)

Returns the cummulative distribution function of a continuous phase-type distribution.

Parameters:	alpha : matrix, shape (1,M) The initial probability vector of the phase-type distribution. A : matrix, shape (M,M) The transient generator matrix of the phase-type distribution. x : vector of doubles The cdf will be computed at these points
Returns:	cdf : column vector of doubles The values of the cdf at the corresponding “x” values

Examples

For Matlab:

>>> a = [0.1,0.9,0];
>>> A = [-6.2, 2, 0; 2, -9, 1; 1, 0, -3];
>>> x = (0.0:0.002:3.0);
>>> cdf = CdfFromPH(a, A, x);
>>> plot(x, cdf)

For Mathematica:

>>> a = {0.1,0.9,0};
>>> A = {{-6.2, 2, 0},{2, -9, 1},{1, 0, -3}};
>>> x = Range[0.0,3.0,0.002];
>>> cdf = CdfFromPH[a, A, x];
>>> ListLinePlot[{Transpose[{x, cdf}]}]

For Python/Numpy:

>>> a = ml.matrix([[0.1,0.9,0]])
>>> A = ml.matrix([[-6.2, 2, 0],[2, -9, 1],[1, 0, -3]])
>>> x = np.arange(0.0,3.002,0.002)
>>> cdf = CdfFromPH(a, A, x)
>>> plt.plot(x, cdf)